Fluid-solid reactions are very important in the chemical and metallurgical process industries. Several models described these reactions such as volume reaction model, grain model, random pore model and nucleation model. These models give two nonlinear-coupled partial differential equations (CPDE). When the fluid concentration is high (for example in liquid-solid reactions), the fluid mass balance must be written as an unsteady equation. There is not any analytical or approximate solution for these equations, due to its complex CPDE. In this work, a new solution technique (quantized method) has been applied to these unsteady state CPDE. The results of this method (conversion-time profiles) have been compared with some existing numerical solutions with a good accuracy. Therefore, this method can be used for rapid estimation of kinetic parameters from experimental data. (C) 2007 Elsevier B.V. All rights reserved.